Certainly! Let's solve the problem step-by-step.
### Given Data:
- The body starts from rest, so the initial velocity (u) is 0 cm/s.
- The acceleration (a) is 20 cm/s².
- The time duration (t) is 8 seconds.
### To Find:
The distance covered by the body in the first 8 seconds.
### Approach:
We can use one of the kinematic equations of motion, which relates distance, initial velocity, acceleration, and time. The equation is:
\(\[ \text{distance} = u \cdot t + \frac{1}{2} \cdot a \cdot t^2 \]\)
Where:
- \(\( u \)\) is the initial velocity.
- \(\( a \)\) is the acceleration.
- \(\( t \)\) is the time duration.
### Step-by-Step Solution:
1. Initial Velocity (u):
Since the body starts from rest:
\(\[ u = 0 \, \text{cm/s} \]\)
2. Acceleration (a):
Given:
\(\[ a = 20 \, \text{cm/s}^2 \]\)
3. Time (t):
Given:
\(\[ t = 8 \, \text{seconds} \]\)
4. Plug the Values into the Equation:
Now we need to substitute the known values into the kinematic equation:
\(\[ \text{distance} = 0 \cdot 8 + \frac{1}{2} \cdot 20 \cdot 8^2 \]\)
5. Calculate the Distance:
\(\[ \text{distance} = 0 + \frac{1}{2} \cdot 20 \cdot 64 \]\)
\(\[ \text{distance} = 10 \cdot 64 \]\)
\(\[ \text{distance} = 640 \]\)
### Final Answer:
The distance covered by the body in the first 8 seconds is 640 cm.
